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arXiv:2007.15842 · Journal of the Optical Society of America B

Scheme for sub-shot-noise transmission measurement using a time-multiplexed single-photon source

Agustina G. Magnoni, Laura T. Knoll, M. A. Larotonda

Published Jul 15, 2021• 2 citations
arXivHTMLPDF

Abstract

Sub-shot-noise performance in transmission measurements can be achieved in optical quantum metrology owing to significantly lower uncertainty in light intensity of quantum beams compared to their classical counterparts. In this work, we simulate the outcome of an experiment that uses a multiplexed single-photon source, considering several types of experimental losses, where we show that the sub-Poissonian statistics of the output is key for achieving sub-shot-noise performance. We compare the numerical results with the shot-noise limit attained using coherent sources and the quantum limit, obtained with an ideal photon-number Fock state. We also investigate conditions in which threshold detectors can be used, as well as the effect of input light fluctuations. Our results show that sub-shot-noise performance can be achieved with improvement factors ranging from 1.5 to 2, even without using number-resolving detectors.

DOI
10.1364/josab.428105

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Sub-shot-noise performance in transmission measurements can be achieved in optical quantum metrology owing to significantly lower uncertainty in light intensity of quantum beams compared to their classical counterparts. In this work, we simulate the outcome of an experiment that uses a multiplexed single-photon source, considering several types of experimental losses, where we show that the sub-Poissonian statistics of the output is key for achieving sub-shot-noise performance. We compare the numerical results with the shot-noise limit attained using coherent sources and the quantum limit, obtained with an ideal photon-number Fock state. We also investigate conditions in which threshold detectors can be used, as well as the effect of input light fluctuations. Our results show that sub-shot-noise performance can be achieved with improvement factors ranging from 1.5 to 2, even without using number-resolving detectors.
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the shot noise limit and reach the Heisenberg limit. Nevertheless, many of those experiments fail to break even the classical shot-noise limit. Following a recent proposal, we present here the results of optical phase measurements with a photon-number resolving detector using coherent states of up to 4200 photons on average. An additional scheme that can be implemented using standard single-photon detectors is also presented, and the results of the two schemes are compared. These measurements present deterministic single-shot sub-wavelength super-resolution up to 288 better than the optical wavelength. The results follow the classically limited sensitivity, up to 86 times better than the wavelength.
Shot noise sets a fundamental limit on the sensitivity of classical optical measurements, with coherent emitters achieving the lowest possible shot-noise level. Emission from sub-Poissonian light provides a pathway to surpass this limit, and single-photon sources provide a natural platform for generating such light. However, it is commonly assumed that continuously excited single-photon sources exhibit Poissonian statistics. In this work, a theoretical model of a continuously driven two-level single-photon source is developed, treating both excitation and radiative decay as stochastic processes. The analysis demonstrates that photon emission can display sub-Poissonian statistics when excitation and decay rates are comparable, showing that continuous excitation does not inherently preclude nonclassical emission. The model is further extended to include finite detection efficiency and detector dead time, illustrating how these practical non-idealities can affect the experimental observation of sub-Poissonian statistics.
Quantum metrology enables us to estimate optical phase shifts beyond the shot noise limit. Applications include quantum-enhanced biological measurement [1], microscopy [2] and gravitational wave detection[3]. For two-mode N-photon system, the NOON state can achieve the highest possible phase sensitivity where multi-photon coherence between two states significantly contributes to improving the phase sensitivity. Another alternative approach to improve the phase sensitivity by use of squeezed states. Squeezing is usually characterized by reducing the quantum noise of desired observable at the expense of increasing the quantum noise for its non-commute partner. Because shot-noise limits the phase sensitivity of any classical states, the reduced quantum noise can be used for improving the phase sensitivity. Here we experimentally study the phase sensitivity of an optical spin-squeezed state by using linear optics. We generated the optical spin-squeezed state using one photon subtraction from a down converted photon source. To implement the sub-shot noise measurement, we used multiplexed photon number resolving detectors so that we can reconstruct the photon number statistics of the state. In the talk, we will analyse the generated state in terms of both squeezing and phase sensitivity by using Fisher information.
Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches [1]. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and materials properties. Without quantum enhancement, the precision limit in optical phase sensing (i.e. the minimum uncertainty) is the shot noise limit (SNL): 1/sqrt(N) where N is the number of resources (e.g. photons) used. Entangled photons promise sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is the NOON state [2], a path-entangled state of definite photon number N. Despite theoretical proposals stretching back decades [3], no measurement using such photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all such demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use the state of art single photon generation and detection technology to respectively make and measure a two-photon NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit — that is, without artificially correcting for loss or any other source of imperfection [4]. We performed a two-photon NOON state polarisation interferometry measurement on a birefringent test phase. We use photons generated from a high-heralding-efficiency, high purity source of telecom-wavelength photon pairs [5], and we employ high efficiency superconducting photon detectors. Unlike previous experiments, our apparatus does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer. Our results show a clear violation (for a range of phases) of the stringent SNL Fisher-information bound, F_{SNL} = 2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms — making our demonstration unconditional. We also performed a direct phase sensing measurement and observed phase uncertainties more than 10 standard deviations below the SNL [4]. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances. References [1] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011). [2] J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [3] R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kołodynski, “Quantum limits in optical interferometry,” Prog. Opt. 60, 345–435 (2015). [4] S. Slussarenko, M. M.Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S.W. Nam, and G. J. Pryde, “Unconditional violation of the shot noise limit in photonic quantum metrology,” Nat. Photon. 11, 700-703 (2017). [5] M. M. Weston, H. M. Chrzanowski, S. Wollmann, A. Boston, J. Ho, L. K. Shalm, V. B. Verma, M. S. Allman, S. W. Nam, R. B. Patel, S. Slussarenko, and G. J. Pryde, “Efficient and pure femtosecond-pulse length source of polarization-entangled photons,” Opt. Express 24, 10,869–10,879 (2016).
The limit of precision in optical measurements is due to quantum fluctuations, which are governed by Poissonian statistics. With a clever setup, however, the authors achieve a precision in transmission measurements that beats this limit, without the selective analysis of recorded data (post-selection). This shows that the single-photon-detector approach, used by many groups worldwide, is viable for real-world optical quantum metrology, not just proof-of-principle tests. In turn, this demonstration unlocks an array of techniques for quantum-state engineering that crucially depend on single-photon detection.
Quantum-intensity-correlated twin beams of light can be used to measure absorption with precision beyond the classical shot-noise limit. The degree to which this can be achieved with a given estimator is defined by the quality of the twin-beam intensity correlations, which is quantified by the noise reduction factor. We derive an analytical model of twin-beam experiments, incorporating experimental parameters such as the relative detection efficiency of the beams, uncorrelated optical noise, and uncorrelated detector noise. We show that for twin beams without excessive noise, measured correlations can be improved by increasing the detection efficiency of each beam; notwithstanding, this may unbalance detection efficiency. However, for beams with excess intensity or other experimental noise, one should balance detection efficiency, even at the cost of reducing detection efficiency—we specifically define these noise conditions and verify our results with statistical simulation. This has application in design and optimization of absorption spectroscopy and imaging experiments.